These matters remind me somewhat of a few late, seminal non-football related generalists and inter-disciplinary thinkers, the economics best seller Small Is Beautful by E.F. Schumacher, as well as the Fable of the Polyploid Horse from Mind and Nature by Gregory Bateson (see below).
http://www.oikos.org/m&nschoolboy.htm
12. SOMETIMES SMALL IS BEATIFUL
Perhaps no variable brings the problems of being alive so vividly and clearly before the analyst's eye as does size. The elephant is afflicted with the problems of bigness; the shrew, with those of smallness. But for each, there is an optimum size. The elephant would not be better off if he were much smaller, nor would the shrew be relieved by being much bigger. We may say that each is
addicted to the size that is.
There are purely physical problems of bigness or smallness, problems that affect the solar system, the bridge, and the wristwatch. But in addition to these, there are problems special to aggregates of living matter, whether these be single creatures or whole cities.
Let us first look at the physical. Problems of mechanical
instability arise because, for example, the forces of gravity do not follow the same quantitative regularities as those of cohesion. A large clod of earth is easier to break by dropping it on the ground than is a small one. The glacier grows and therefore, partly melting and partly breaking, must begin a changed existence in the form of avalanches, smaller units that must fall off the larger matrix. Conversely, even in the physical universe, the very small may become unstable because the relation between surface area and weight is nonlinear. We break up any material which we wish to dissolve because the smaller pieces have a greater ratio of surface to volume and will therefore give more access to the solvent. The larger lumps will be the last to disappear. And so on.
To carry these thoughts over into the more complex world of living things, a fable may be offered:
THE TALE OF THE POLYPLOID HORSE
The fable shows what inevitably happens when two or more variables, whose curves are discrepant, interact. That is what produces the interaction between change and tolerance. For instance, gradual growth in a population, whether of automobiles or of people, has no perceptible effect upon a transportation system until suddenly the threshold of tolerance is passed and the traffic jams. The changing of one variable exposes a critical value of the other.
They say the Nobel people are still embarrassed when anybody mentions polyploid horses. Anyhow, Dr. P. U. Posif, the great Erewhonian geneticist, got his prize in the late 1980s for jiggling with the DNA of the common cart horse (
Equus caballus). It was said that he made a great contribution to the then new science of transportology. At any rate, he got his prize for
creating - no other word would be good enough for a piece of applied science so nearly usurping the role of deity - creating, I say, a horse precisely twice the size of the ordinary Clydesdale. It was twice as long, twice as high, and twice as thick. It was a polyploid, with four times the usual number of chromosomes.
P.U. Posif always claimed that there was a time, when this wonderful animal was still a colt, when it was able to stand on its four legs. A wonderful it must have been! But anyhow, by the time the horse was shown to the public and recorded with all the communicational devices of modern civilization, the horse was not doing any standing. In a word, it was
too heavy. It weighed, of course, eight times as much as a normal Clydesdale.
For a public showing and for the media, Dr. Posif always insisted on turning off the hoses that were continuously necessary to keep the beast at normal mammalian temperature. But we were always afraid that the innermost parts would begin to cook. After all, the poor beast's skin and dermal fat were twice as thick as normal, and it surface area was only four times that of a normal horse, so it didn't cool properly.
Every morning, the horse had to be raised to its feet with the aid of a small crane and hung in a sort of box on wheels, in which it was suspended on springs, adjusted to take half its weigh off its legs.
Dr. Posif used to claim that the animal was outstandingly intelligent. It had, of course, eight times as much brain (by weight) as any other horse, but I could never see that it was concerned with any questions more complex than those which interest other horses. I had very little free time, what with one thing and another - always panting, partly to keep cool and partly to oxygenate its eight-times body. Its windpipe, after all, had only four times the normal area of cross section.
And then there was eating. Somehow it had to eat, every day, eight times the amount that would satisfy a normal horse and had to push all that food down an esophagus only four times the caliber of the normal. The blood vessels, too, were reduced in relative size, and this made circulation more difficult and put extra strain on the heart.
A sad beast.
Of all such cases, the best known today is the behavior of fissionable material in the atom bomb. The uranium occurs in nature and is continually undergoing fission, but no explosion occurs because no chain reaction is established. Each atom, as it breaks, gives off neutrons that, that if they hit another uranium atom, may cause fission, but many neutrons are merely lost. Unless the lump of uranium is of critical size, an average of less than one neutron from each fission will break another atom, and the chain will dwindle. If the lump is made bigger, a larger fraction of the neutrons will hit uranium atoms to cause fission. The process will then achieve positive exponential gain and become an explosion.
In the case of the imaginary horse, length, surface area, and volume (or mass) become discrepant because their curves of increase have mutually nonlinear characteristics. Surface varies as the square of length, volume varies as the cube of length, and surface varies as the 2/3 power of volume.
For the horse (and for all real creatures), the matter becomes more serious because to remain alive, many internal motions must be maintained. There is an internal logistics of blood, food, oxygen, and excretory products and a logistics of information in the form of neural and hormonal messages.
The harbor porpoise, which is about three feet long, with a jacket of blubber about one inch thick and a surface area of about six square feet, has a known heat budget that balances comfortably in Arctic waters. The heat budget of a big whale, which is about ten times the length of the porpoise (i.e. 1,000 times the volume and 100 times the surface), with a blubber jacket nearly twelve inches thick, is totally mysterious. Presumably, they have a superior logistic system moving blood through the dorsal fins and tail flukes, where all cetaceans get rid of heat.
The fact of growth adds another order of complexity to the problems of bigness in living things. Will growth alter the proportions of the organism? These problems of the limitation of growth are met in very different ways by different creatures.
A simple case is that of the palms, which do not adjust their girth to compensate for their height. An oak tree with growing tissue (cambium) between its wood, and its bark grows in length and width throughout its life. But a coconut palm, whose only growing tissue is the apex of the trunk (the so-called millionaire's salad, which can only be got at the price of killing the palm), simply gets taller and taller, with some slow increase of the bole at its base. For this organism, the limitation of height is simply a normal part of its adaptation of a niche. The sheer mechanical instability of excessive height without compensation in girth provides its normal way of death.
Many plants avoid (or solve?) these problems of the limitation of growth by linking their life-span to the calendar or to their own reproductive cycle. Annuals start a new generation each year, and plants like the so-called century plant (yucca) may live many years but, like the salmon, inevitably die when they reproduce. Except for multiple branching within the flowering head, the yucca makes no branches. The branching influorescence itself is its terminal stem; when that has completed its function, the plant dies. Its death is normal to its way of life.
Among some higher animals, growth is controlled. The creature reaches a size or age or stage at which growth simply stops (i.e., is stopped by chemical or other messages within the organization of the creature). The cells, under control, cease to grow and divide. When controls no longer operate (by failure to generate the message or failure to receive it), the result is cancer. Where do such messages originate, what triggers their sending, and in what presumably chemical code are these messages immanent? What controls the nearly perfect external bilateral symmetry of the mammalian body? We have remarkably little knowledge of the message system that controls growth. There must be a whole interlocking system as yet scarcely studied.
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